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M. Fischermann, A. Hoffmann, D. Rautenbach, L. A. Székely and L. Volkmann, “Wiener Index versus Maximum Degree in Trees,” Discrete Applied Mathematics, Vol. 122, No. 1-3, 2002, pp. 127-137. doi:10.1016/S0166-218X(01)00357-2

has been cited by the following article:

• TITLE: Cycles, the Degree Distance, and the Wiener Index

  AUTHORS: Daniel Gray, Hua Wang

  KEYWORDS: Degree Distance; Wiener Index; Cacti

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.2 No.4, November 1, 2012

  ABSTRACT: The degree distance of a graph G is , where and are the degrees of vertices , and is the distance between them. The Wiener index is defined as . An elegant result (Gutman; Klein, Mihali?,, Plav?i? and Trinajsti?) is known regarding their correlation, that for a tree T with n vertices. In this note, we extend this study for more general graphs that have frequent appearances in the study of these indices. In particular, we develop a formula regarding their correlation, with an error term that is presented with explicit formula as well as sharp bounds for unicyclic graphs and cacti with given parameters.